Whole angle MEMS gyroscope

ABSTRACT

According to one aspect, embodiments herein provide a gyroscope comprising a central anchor, a plurality of internal flexures, a plurality of masses, each mass coupled to the central anchor via at least one of the plurality of internal flexures and configured to translate in a plane of the gyroscope, and a plurality of mass-to-mass couplers, each mass-to-mass coupler coupled between two adjacent masses of the plurality of masses, and a plurality of transducers, each configured to perform at least one of driving and sensing motion of a corresponding one of the plurality of masses, wherein the plurality of transducers is configured to drive the plurality of masses in at least a first vibratory mode and a second vibratory mode.

CROSS-REFERENCE TO RELATED APPLICATIONS

The presented application claims priority under 35 U.S.C. § 119(e) toU.S. Provisional Application Ser. No. 62/165,365, filed on May 22, 2015,entitled WHOLE ANGLE MEMS GYROSCOPE, which is hereby incorporated hereinby reference.

BACKGROUND OF THE INVENTION

The present disclosure generally relates to vibrating structuregyroscopes and more specifically to Microelectromechanical System (MEMS)based vibrating structure gyroscopes. Vibrating structure gyroscopesutilize solid-state resonators, of different shapes, to measureorientation or rotation rate based on the principle that a vibratingobject tends to continue vibrating (i.e., oscillate) in a fixedorientation in space as its support rotates, and any vibrationaldeviation of the object can be used to derive a change in direction.Vibrating structure gyroscopes may be manufactured with MEMS basedtechnology. For example, vibrating structure gyroscopes may befabricated on silicon or glass wafers using a sequence of stepsincluding photolithography, etching and deposition, or any other MEMSbased technology.

Vibrational deviations in a resonator of a MEMS based gyroscope may becaused by a Coriolis force. For example, a mass moving at a givenvelocity will experience Coriolis acceleration when the mass is alsorotated with an angular velocity. The Coriolis acceleration isperpendicular to the velocity and the angular velocity. The Coriolisacceleration vector is given by a_(c)=−2(v×Ω), where v is the velocityvector and Ω is the angular velocity vector. Coriolis acceleration isthus indicative of the angular velocity of rotation.

Many MEMS based gyroscopes are configured to operate in a rate mode. Ina rate mode of operation, vibration of one axis (i.e., a drive axis) ofa MEMS based gyroscope is driven at a fixed amplitude in a closed loopwhile Coriolis-induced motion is read out on the other axis (i.e., asense axis). In such a rate mode, the amplitude of the Coriolis-inducedmotion read out on the sense axis is indicative of a rate of angularmovement of the gyroscope. Rate mode operated gyroscopes are limited inthat the Coriolis-induced motion measurements are limited by the dynamicrange of the open-loop sense axis. For fast movements of the gyroscope,the open-loop sense axis may not be able to “keep up” with the movementof the gyroscope. In addition, spring non-linearities at high rates ofrotation may cause errors. Some MEMS based gyroscopes operated in ratemode attempt to avoid these problems by also operating the sense axis ina closed loop and monitoring the level of force required to maintain theamplitude of the sense axis at a fixed level. However, such gyroscopesare limited by the closed sense loop bandwidth and the maximum forcecapable of being exerted by the rebalance.

One example of a MEMS based gyroscope configured to operate in a ratemode is a Tuning Fork (TF) gyroscope. A Tuning Fork gyroscope includes apair of relatively large lumped-element proof masses that are driven tooscillate, in an in-plane axis, with equal amplitude but in oppositedirections. When a TF gyroscope is rotated, the Coriolis force createsan orthogonal vibration (i.e., an out-of-plane vibration) in the proofmasses that can be sensed by a variety of mechanisms. By monitoringout-of-plane vibrations of the proof masses, the rate of rotation of theTF gyroscope can be determined.

Another mode of operation for MEMS based gyroscopes is a whole anglemode (otherwise known as an integrating or rate integrating mode). In awhole angle mode of operation, two axes, having identical frequency anddamping, are coupled by Coriolis motion. The axes are driven such thatthe total vibrational amplitude of the two axes is sustained, but thedistribution of energy between the two axes is allowed to change freely.Accordingly, a Coriolis force causes energy to be transferred from oneaxis to the other as the gyroscope rotates. By measuring thedistribution of energy between the axes, an angle of rotation (withrespect to a starting angle) can be read out. As energy can freelytransfer from one axis to the other in a MEMS based gyroscope operatingin whole angle mode, there is no limit on the rate at which the axes cantransfer motion. As such, whole angle operating gyroscopes avoid thedynamic range issues discussed above with regard to rate mode operatinggyroscopes and typically provide a higher level of performance andhigher bias stability.

One important requirement of a whole angle operating MEMS basedgyroscope is that the two modes be identical (i.e., degenerate) withregard to frequency and damping. If the frequencies differsubstantially, a Coriolis force caused by rotation of the gyroscope willnot be sufficient to transfer energy from one mode to the other and thevibration will stay “locked” to a single axis. This will interfere withthe free transfer of motion between modes and the free precession of themode shape of the gyroscope. A whole angle operating MEMS basedgyroscopes must therefore be designed and fabricated with exceptionalsymmetry and with mode structures that are insensitive to expectedfabrication variations. In addition, it is also typically desired forwhole angle operating MEMS based gyroscopes to provide low damping(i.e., long ring down time) and matched damping for principle axes. Thisis because low overall damping correlates to low damping differencesbetween the two axes and on-axis damping may result in gyroscope biaswhen drive forcers are misaligned. A mismatch (or mismatch drift) mayresult in a bias (or bias drift).

Traditional whole angle MEMS based gyroscopes include an axially orcylindrically symmetric and continuous structure that is driven toexcite two vibratory modes of the structure (i.e., an n=2 vibratory modewhere two points of the ring are moving away from the center of the ringwhile two other points of the ring are moving toward the center of thering). Rotation of the gyroscope results in a Coriolis force that causesmovement (i.e., either inward or outward motion) of other points of thesymmetric structure. By monitoring the movement of the symmetricstructure in two in-plane axes, the angle of rotation of the gyroscopecan be determined.

One common example of a whole angle operating gyroscope is aHemispherical Resonator Gyroscope (HRG) (otherwise known as a wine-glassgyroscope). An HRG includes a thin hemispherical shell, anchored by astem. The shell is driven to a flexural resonance and a gyroscopiceffect is obtained from the inertial property of resulting flexuralstanding waves. An HRG is typically reliable and accurate; however, theyare also typically large and costly.

Another example of a whole angle operating gyroscope is a ringgyroscope. Ring gyroscopes include axially symmetric and continuousrings that are driven in an n=2 vibratory mode, as discussed above. Themovement of the ring is monitored to determine an angle of rotation ofthe ring gyroscope. The performance of such ring gyroscopes is limitedin that due to the limited mass of the rings, the sensitivity of thegyroscope is relatively low and the bias instability is relatively high.

SUMMARY

A new MEMS based gyroscope design is provided that combines the bestfeatures of a lumped-element TF gyroscope and a rotationally symmetricgyroscope. Certain embodiments efficiently use relatively large masses(e.g., like a TF gyroscope) supported by relatively weak flexures toprovide low damping and hence high sensitivity while maintaining aneight-fold symmetry conducive to the n=2 vibratory mode used in mostwhole angle based gyroscopes to provide high dynamic range. As discussedin more detail below, certain embodiments are capable of operating inboth rate and whole angle mode, are low cost, and are easily fabricated.

One aspect of the present disclosure is directed to a gyroscopecomprising a central anchor, a plurality of internal flexures, aplurality of masses, each mass coupled to the central anchor via atleast one of the plurality of internal flexures and configured totranslate in a plane of the gyroscope, and a plurality of mass-to-masscouplers, each mass-to-mass coupler coupled between two adjacent massesof the plurality of masses, and a plurality of transducers, eachconfigured to perform at least one of driving and sensing motion of acorresponding one of the plurality of masses, wherein the plurality oftransducers is configured to drive the plurality of masses in at least afirst vibratory mode and a second vibratory mode.

According to one embodiment, each transducer is located at a peripheryof the corresponding one of the plurality of masses. In anotherembodiment, at least one transducer is configured to electrostaticallydrive motion of its corresponding one of the plurality of masses. In oneembodiment, at least one transducer is configured to magnetically drivemotion of its corresponding one of the plurality of masses. In anotherembodiment, at least one transducer is configured to optically drivemotion of its corresponding one of the plurality of masses. In oneembodiment, at least one transducer is configured to piezoelectricallydrive motion of its corresponding one of the plurality of masses. Inanother embodiment, at least one transducer is configured to thermallydrive motion of its corresponding one of the plurality of masses.

According to another embodiment, the plurality of transducers is furtherconfigured to drive the plurality of masses in an n=2 vibratory mode. Inone embodiment, the first vibratory mode and the second vibratory modeare 45° apart. In another embodiment, the plurality of transducers isfurther configured to drive motion of the plurality of masses at a fixedamplitude in the first vibratory mode and to sense motion of theplurality of masses in the second vibratory mode. In one embodiment, thegyroscope further comprises a controller coupled to the plurality oftransducers, wherein the plurality of transducers is further configuredto provide signals to the controller based on the sensed motion of theplurality of masses in the second vibratory mode, and wherein thecontroller is configured to calculate a rate of rotation of thegyroscope based on the signals.

According to one embodiment, the plurality of transducers is furtherconfigured to drive motion of the plurality of masses such that a totalvibrational energy is maintained across the first vibratory mode and thesecond vibratory mode and to sense a distribution of energy between thefirst vibratory mode and the second vibratory mode. In anotherembodiment, the gyroscope further comprises a controller coupled to theplurality of transducers, wherein the plurality of transducers isfurther configured to provide signals to the controller based on thesensed distribution of motion between the first vibratory mode and thesecond vibratory mode, and wherein the controller is configured tocalculate an angle of rotation of the gyroscope based on the signals.

According to another embodiment, each mass-to-mass coupler includes abar coupled to each adjacent mass via a flexural hinge, wherein the baris configured to operate such that circumferential motion of one of thetwo adjacent masses of the plurality of masses to which it is coupleddepends on radial motion of the other one of the two adjacent masses.

According to one embodiment, the gyroscope further comprises a pluralityof outside anchors, a plurality of outside shuttles, each located at aperiphery of a corresponding one of the plurality of masses, and aplurality of outside flexures, wherein each mass of the plurality ofmasses is suspended between the central anchor and the plurality ofoutside anchors via the plurality of internal flexures and the pluralityof outside flexures, and wherein each one of the plurality of outsideshuttles is configured to restrict rotation of its corresponding one ofthe plurality of masses. In one embodiment, each one of the plurality ofoutside shuttles is further configured to decouple x- and y-motion ofits corresponding one of the plurality of masses. In another embodiment,each one of the plurality of outside shuttle is further configured toprevent force from being applied circumferentially to its correspondingone of the plurality of masses.

According to another embodiment, the gyroscope further comprises aplurality of internal shuttles, each one of the plurality of internalshuttles coupled between the central anchor and a corresponding one ofthe plurality of masses and configured to restrict rotation of itscorresponding one of the plurality of masses. In one embodiment, eachone of the plurality of internal shuttles is further configured todecouple x- and y-motion of its corresponding one of the plurality ofmasses.

According to one embodiment, the gyroscope further comprises a pluralityof angled electrodes, each angled electrode coupled to a correspondingone of the plurality of masses and configured to trim the cross springterm of the corresponding one of the plurality of masses. In oneembodiment, in trimming the cross spring term of its corresponding oneof the plurality of masses, each angled electrode is configured togenerate a radial force component in the second vibratory mode inresponse to a circumferential motion of its corresponding one of theplurality of masses in the first vibratory mode, and generate acircumferential force component in the second vibratory mode in responseto a radial motion of its corresponding one of the plurality of massesin the first vibratory mode, wherein the radial force component and thecircumferential force component are configured to either assist oroppose the vibration of the plurality of masses in the second vibratorymode to trim the cross spring term.

According to another embodiment, the gyroscope is implemented on a cubiccrystal based substrate having a (100) direction plane and a (110)direction plane, and wherein at least one of the plurality of internalflexures is oriented equidistant from the (100) direction plane and the(110) direction plane. In one embodiment, the at least one of theplurality of internal flexures is oriented 22.5° from the (100)direction and the (110) direction. In another embodiment, the cubiccrystal-based substrate is a Silicon (Si) based substrate.

According to one embodiment, the plurality of masses includes aplurality of wedge-shaped masses. In another embodiment, the pluralityof masses is arranged symmetrically about the central anchor. In oneembodiment, the gyroscope has a thickness, and the plurality of internalflexures includes flexures having a width that is at least five timesnarrower than the thickness of the gyroscope. In another embodiment, thegyroscope is a Microelectromechanical System (MEMS) based gyroscope.

Another aspect of the present disclosure is directed to a gyroscopecomprising a central anchor, a plurality of internal flexures, aplurality of masses, each mass coupled to the central anchor via one ofthe plurality of internal flexures and configured to translate in aplane of the gyroscope, means for driving the plurality of masses in avibratory mode emulating the n=2 vibratory mode of a rotationallysymmetric gyroscope, and means for operating the gyroscope in one of arate mode of operation and a whole angle mode of operation.

According to one embodiment, the gyroscope further comprises means fordecoupling radial and circumferential motion of each one of theplurality of masses. In another embodiment, the gyroscope furthercomprises means for trimming a cross spring term of the gyroscope.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of at least one embodiment are discussed below withreference to the accompanying figures, which are not intended to bedrawn to scale. The figures are included to provide illustration and afurther understanding of the various aspects and embodiments, and areincorporated in and constitute a part of this specification, but are notintended as a definition of the limits of the invention. In the figures,each identical or nearly identical component that is illustrated invarious figures is represented by a like numeral. For purposes ofclarity, not every component may be labeled in every figure. In thefigures:

FIG. 1 is a diagram illustrating one embodiment of a MEMS basedgyroscope according to aspects of the present invention;

FIG. 2 is a diagram of an internal flexure according to aspects of thepresent invention;

FIG. 3 is a diagram of an outer flexure according to aspects of thepresent invention;

FIG. 4 is a diagram illustrating two degenerate vibratory modes of aMEMS based gyroscope according to aspects of the present invention;

FIG. 5A is a diagram illustrating one embodiment of a K_(xy) trimelectrode and a mass-to-mass coupler according to aspects of the presentinvention;

FIG. 5B is a diagram illustrating directional planes of a cubic crystalstructure according to aspects of the present invention;

FIG. 5C is a diagram illustrating one embodiment of the orientation of aMEMS based gyroscope relative to the crystallographic orientation of acubic crystal structure according to aspects of the present invention;

FIG. 5D is a diagram illustrating another embodiment of the orientationof a MEMS based gyroscope relative to the crystallographic orientationof a cubic crystal structure according to aspects of the presentinvention;

FIG. 6A is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 6B is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 6C is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 6B according to aspects of the presentinvention;

FIG. 6D is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 6E is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 6D according to aspects of the presentinvention;

FIG. 6F is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 7A is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 7B is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 8 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 9 is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 8 according to aspects of the present invention;

FIG. 10 is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 8 according to aspects of the present invention;

FIG. 11 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 12 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 13 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 14 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 15 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 16 is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 15 according to aspects of the presentinvention;

FIG. 17A is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention;

FIG. 17B is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 17A according to aspects of the presentinvention;

FIG. 17C is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 17A according to aspects of the presentinvention;

FIG. 18 is a diagram of another embodiment of a MEMS based gyroscopeaccording to aspects of the present invention; and

FIG. 19 is a diagram illustrating further detail of the MEMS basedgyroscope shown in FIG. 18 according to aspects of the presentinvention.

DETAILED DESCRIPTION

Aspects and embodiments described herein provide a MEMS based gyroscopedesign that combines the best features of a TF gyroscope and arotationally symmetric gyroscope. Certain embodiments efficiently userelatively large masses (e.g., similar to a TF gyroscope) to providehigh sensitivity while maintaining an eight-fold symmetry conducive tothe n=2 vibratory mode used in most whole angle based gyroscopes toprovide high dynamic range. Certain embodiments are capable of operatingin both rate and whole angle mode, may be low cost, and may be easilyfabricated.

It is to be appreciated that embodiments of the methods and apparatusesdiscussed herein are not limited in application to the details ofconstruction and the arrangement of components set forth in thefollowing description or illustrated in the accompanying drawings. Themethods and apparatuses are capable of implementation in otherembodiments and of being practiced or of being carried out in variousways. Examples of specific implementations are provided herein forillustrative purposes only and are not intended to be limiting. Also,the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use herein of“including,” “comprising,” “having,” “containing,” “involving,” andvariations thereof is meant to encompass the items listed thereafter andequivalents thereof as well as additional items. References to “or” maybe construed as inclusive so that any terms described using “or” mayindicate any of a single, more than one, and all of the described terms.

Referring to FIG. 1, there is illustrated one embodiment of a MEMS basedgyroscope 100 configured according to aspects of the present disclosure.The gyroscope 100 includes eight wedge-shaped masses 102, internalflexures 104, outer flexures 106, a central anchor 110, outer anchors114, outer shuttles 112, inner shuttles 113, and mass-to-mass couplers108.

Each mass 102 is suspended between an inner shuttle 113 and an outershuttle 112 via internal flexures 104 and outer flexures 106 and isconfigured to translate in the plane of the gyroscope 100 on theflexures 104, 106. An internal flexure 104 is shown in greater detail inFIG. 2 and an outer flexure 106 is shown in greater detail in FIG. 3.According to one embodiment (shown in FIGS. 2 and 3) where the gyroscope100 is fabricated on a silicon wafer, the internal flexures 104 andouter flexures 106 include areas of silicon 105 defined by slots 107(i.e., areas of empty space) in the silicon that are configured to allowa coupled mass 102 to vibrate (i.e., translate) in the plane of thegyroscope 100. In other embodiments, the flexures 104, 106 may beconstructed differently. The central anchor 110 and the outer anchors114 are configured to support the structure. The mass-to-mass couplers108 are coupled between adjacent masses 102.

Each internal shuttle 113 and outer shuttle 112 is configured to enforceradial forcing on its corresponding mass 102 and restrict rotation ofits corresponding mass 102 by decoupling x- (i.e., radial) and y- (i.e.,circumferential) motion. For example, each outer shuttle 112 isconfigured to only move radially (i.e., in a direction 115 in towardsthe anchor or out away from the anchor 110) and each inner shuttle 113is configured to move only circumferentially (i.e., in direction 119)around the anchor 110. Accordingly, each mass 102 may only translate inthe plane of the gyroscope 100 (i.e. move radially and/orcircumferentially in the plane of the gyroscope 100). By decoupling thex- and y-motion, the stiffness of each direction may be designedindependently. Also, out-of-plane motion may be suppressed by utilizingflexures of high aspect ratio (i.e. whose width is at least five timesnarrower than the thickness of the flexure for the whole planargyroscope 100). For example, a gyroscope that is 100 microns inthickness may utilize flexures which are five times narrower (e.g., 20microns wide), ten times narrower (e.g., 10 microns wide), or twentytimes narrower (5 microns wide). In addition, each outer shuttle 112 mayalso reduce errors caused by misaligned drive/sense transducer 116electrodes by being stiff in the direction of the misaligned forcecomponent (i.e., by only moving radially in and out, the outer shuttle112 reduces any erroneous circumferential forces on the mass 102 fromthe drive).

The gyroscope 100 also includes drive/sense transducers 116. For theease of illustration, only one drive/sense transducer 116 is shown inFIG. 1; however, a drive/sense transducer 116 is located at theperiphery of each mass 102 in the gyroscope 100. Each drive/sensetransducer 116 is capable of driving motion of its corresponding mass102 and of sensing motion of its corresponding mass 102. For example, inat least one embodiment, each drive/sense transducer 116 is anelectrostatic transducer (e.g., a variable capacitor) that includes anelectrode positioned at the periphery of a corresponding mass 102 and anelectrode positioned on a corresponding outer shuttle 112. When avoltage is applied to the electrode at the periphery of the mass 102,motion of the mass is electrostatically driven. Each drive/sensetransducer 116 is also configured to sense motion of its correspondingmass and provide a signal indicative of the motion to an externalcontroller/processor 117. According to one embodiment, the drive/sensetransducers 116 are clapper or comb drives; however, in otherembodiments, any other appropriate type of circuit capable of drivingand sensing motion of a mass 102 may be utilized. For example, in otherembodiments, magnetic, piezoelectric, thermal, or optical basedtransducers may be utilized.

As discussed above, the drive-sense transducers 116 are located at theperiphery of each mass 102; however, in other embodiments, a transducer116 may be located at any other position adjacent a mass 102. Inaddition, according to at least one embodiment, each drive-sensetransducer 116 is located internal to a mass 102.

As also discussed above, a single transducer 116 is associated with eachmass 102; however, in other embodiments, each mass 102 may be associatedwith more than one transducer 116. For example, in at least oneembodiment, each mass 102 is associated with a first transducer thatdrives motion of the mass 102 and a second transducer that senses motionof the mass 102. In another embodiment, each mass 102 also includes athird transducer that is utilized for tuning the mass 102 (e.g., tuningthe radial spring constant of the mass 102). In other embodiments, thetransducer(s) 116 associated with each mass 102 may be configured in anyappropriate way to drive motion of the mass 102, sense motion of themass 102, and/or tune the mass 102.

As the masses 102 in the gyroscope 100 vibrate, the mass-to-masscouplers 108 couple the motion of the masses 102 together, resulting inan n=2 vibratory mode resembling that of a rotationally symmetricgyroscope (e.g., a ring, disc, or hemispherical gyroscope). FIG. 4 is adiagram illustrating two degenerate vibratory modes (a first vibratorymode 400 and a second vibratory mode 420) of the gyroscope 100.Considering the first vibratory mode 400, if the gyroscope 100 is notrotating, two of the masses 405 are translating inwardly and two of themasses 403 are translating outwardly. As shown in FIG. 4, the first n=2vibratory mode shape 400 of the gyroscope is an ellipse 402 a. Due tothe mass-to-mass couplers 108, the other four masses 407, 409 aretranslating circumferentially. Resulting velocity vectors 404 are alsoshown for each mass. Considering the second vibratory mode 420, if thegyroscope 100 is not rotating, two of the masses 407 are translatinginwardly and two of the masses 409 are translating outwardly. As shownin FIG. 4, the second n=2 vibratory mode shape 420 of the gyroscope isan ellipse 402 b that is rotated 45° in relation to ellipse 402 a of thefirst vibratory mode 400. Due to the mass-to-mass couplers 108, theother four masses 403, 405 are translating circumferentially. Resultingvelocity vectors 404 are also shown for each mass.

As the gyroscope 100 is rotated (e.g., due to rotation of the system towhich the gyroscope 100 is attached) about axis (Z) which isperpendicular to the plane of the gyroscope 100, the vibratory modes400, 420 exhibit coupling via Coriolis forces. For example, as shown inFIG. 4, the Coriolis forces 406 (F_(c)=−2mΩ×v) in the first vibratorymode 400 arising from the velocity vectors 404 force two masses 407inward and two masses 409 outward, thus exciting the other vibratorymode 420.

The Coriolis forces 406 of the first vibratory mode 400 remove energyfrom the first vibratory mode 400 and excite motion in the secondvibratory mode 420. For example, as shown in FIG. 4, the Coriolis force406 applied to each mass in the first vibratory mode 400 correspond tothe displacement of the mass in the second vibratory mode 420.Therefore, the Coriolis forces 406 resulting from the rotation of thegyroscope 100 result in the transfer of energy from the first vibratorymode 400 to the second vibratory mode 420. Similarly, Coriolis forces ofthe second vibratory mode 420 reduce motion in the second vibratory mode420 and excite motion in the first vibratory mode 400. Therefore, theCoriolis forces resulting from the rotation of the gyroscope 100 alsoresult in the transfer of energy from the second vibratory mode 420 tothe first vibratory mode 400.

More specifically, the vibratory motion in each mode 400, 420 issinusoidal and as shown in the first vibratory mode 400 of FIG. 4, themasses 403 and 405 are at one extreme of their displacement (i.e., theoutwardly moving masses 403 are at their largest radial distance and theinwardly moving masses 405 are at their smallest radial distance). At atime T/2=1/(2*f), where f is the frequency of the first vibratory mode400 (T=1/f is the period and w=2πf is the frequency in radians persecond), the masses 403 are closer to the center and the masses 405 arefarther from the center. Accordingly, the position of each mass at anytime is related to the phase of the oscillation at that time. In otherwords, if r403 is the radial position of masses 403 and r405 is theradial position of masses 405, then r403=r0*sin (wt) and r405=r0*sin(wt+π).

The velocity of each mass is out of phase with the displacement by π/2.Therefore, when a mass 403 is at the outward extreme (as shown in FIG.4), its velocity is actually zero. The velocity vector 404 for each massshown in FIG. 4 is actually the velocity at a timet=(π/2w)=1/(4*f)=(T/4) seconds ago. As such, the velocity of a mass 403can be expressed as v403=v0*sin(wt+π/2)=r0w*cos (wt), and the velocityof a mass 405 can be expressed as v405=v0*sin(wt+3π/2)=r0w*cos (wt+π).These velocity equations show that in addition to the displacementvectors, the velocity vectors also reverse direction sinusoidally. Forexample, at each half cycle, the velocity vectors reverse direction. Thecorresponding Coriolis force vectors also reverse direction at each halfcycle. This is necessary to excite motion in the other mode, as theother mode also has sinusoidal motion which requires sinusoidal forcing.In at least one embodiment, it is desired to set the frequency of theforce sinusoid equal to the resonance frequency of the mode beingexcited. By setting these frequencies equal, stronger coupling of themodes may be achieved.

With reference to the first vibratory mode 400 of FIG. 4, the positionsof each mass 403, 405, 407, 409 are shown when the masses 403 and 405are at one extreme of their displacement and the velocity 404 andCoriolis vectors 406 are shown at a time T/4 seconds earlier. The timeat which the Coriolis force vectors 406 are shown in the first vibratorymode 400 is the same time at which the velocity vectors 404 are shown inthe second vibratory mode 420 (the force is in phase with the velocityof the vibratory motion which is increasing, i.e., the force counteractsdamping, which is proportional to velocity), which is again T/4 secondsearlier than the time corresponding to the position of the masses 403,405, 407, 409 in the second vibratory mode 420. In other words thevelocity vectors 404 and force vector 406 shown in each vibratory mode400, 420 are shown at the same time.

As the Coriolis forces 406 in the first vibratory mode 400 excite themasses in the second vibratory mode 420 (i.e., assist the velocityvectors 404 in the second vibratory mode 420), the Coriolis forces 406in the second vibratory mode 420 reduce the motion in the firstvibratory mode 400 (i.e., are opposed to the velocity vectors 404 in thefirst vibratory mode 400). As such, energy is transferred from the firstvibratory mode 400 to the second vibratory mode 420. At some point, allof the energy will have transferred and the motion in the firstvibratory mode 400 will be zero.

At this point, the Coriolis forces 406 in the second vibratory mode 420remain the same, but are now working with zero velocity in the firstvibratory mode 400. The Coriolis forces 406 excite the motion shown inthe first vibratory mode 400, but with a phase difference of π.Accordingly, the time at which the velocity vectors 404 are as shown inthe first vibratory mode 400 of FIG. 4 is T/2 different than aspreviously discussed. This means that the Coriolis force vectors 406 inthe first vibratory mode 400 also reverse direction, thus reducingmotion in the second vibratory mode 420. As such, energy is transferredback to the first vibratory mode 400 from the second vibratory mode 400.It is to be appreciated that one complete cycle of energy transfer(i.e., the first vibratory mode 400 to the second vibratory mode 420 andback to the first vibratory mode 400) results in a phase shift of 7E inthe vibratory oscillation. The next half cycle (i.e., the firstvibratory mode 400 to the second vibratory mode 420) will likewiseresult in motion in the second vibratory mode 420 that is π differentthan before.

The transfer of energy between modes can also appear similar to arotation of the modal shape (i.e., the second vibratory mode 420 appearsas a 45° rotated version of the first vibratory mode 400). It is to beappreciated that, from a frame of reference affixed to the gyroscope100, the gyroscope structure 100 does not rotate; rather, theorientation of the overall vibratory mode (superposition of modes 400and 420 in varying proportions) appears to rotate in that frame as thatframe of reference is rotated. At overall vibratory mode orientationsbetween 45°, some combination of the two modes 400 and 420 will appear,i.e. all masses will be moving both radially and circumferentially, inproportion to the angular distance between the current orientation andthe starting orientation. For rate mode operation, the control commandsexert rebalancing forces to null (maintain at zero) the radial motion ofeither masses 407, 409 or masses 403, 405. For whole angle modeoperation, the exchange of energy (or apparent rotation of the overallvibratory mode) is allowed to occur without interference. Because ofdamping, forces must be continually applied along the direction oflargest motion (or the direction of the overall vibratory mode), whichis accomplished by applying the appropriate proportion of force(determined by the vector components of the orientation) via both thetransducers 116 located at the masses 407, 409 and the masses 403, 405.

By monitoring the motion of the masses 102 in the gyroscope 100 therotation of the gyroscope 100 can be determined. For example, in a ratemode of operation of the gyroscope 100, one of the modes (e.g., thefirst vibratory mode 400 or the second vibratory mode 420) iscontinually driven at a fixed amplitude by the drive/sense transducers116, and the motion of the other mode is monitored, by the drive/sensetransducers 116. Signals from the drive/sense transducers 116 based onthe sensed motion are provided to the controller 117 (coupled to thedrive/sense transducers 116) and the controller 117 can determine a rateof rotation of the gyroscope 100 based on the signals. For example, inone embodiment, the motion of masses 102 in one mode (e.g., the firstvibratory mode 400 or the second vibratory mode 420) is driven at afixed amplitude (by the drive/sense transducers 116) while the othermode is measured (by the drive/sense transducers 116) in an open loop.In such an embodiment, the amplitude of motion sensed by the drive/sensetransducers 116 is proportional to the rate of rotation of thegyroscope. In another embodiment, the motion of masses 102 in one mode(e.g., the first vibratory mode 400 or the second vibratory mode 420) isdriven at a fixed amplitude (by the drive/sense transducers 116) whilethe motion of masses 102 in the other mode is fixed at zero, by thedrive/sense transducers 116, in a closed-loop. The required feedbackforce necessary to maintain the motion of the masses 102 at zero isproportional to the rate of rotation of the gyroscope 100.

In a whole-angle mode of operation, the motion of masses 102 in bothmodes 400, 420 is driven by the drive/sense transducers 116 such thatthe total vibrational amplitude of the masses 102 across both modes 400,420 is sustained, but the distribution of energy between the two modes400, 420 is allowed to change freely. By measuring the distribution ofmotion between the modes 400, 420 with the drive/sense transducers 116and providing signals based on the distribution of motion to thecontroller 117, an angle of rotation (with respect to a starting angle)can be read out by the controller 117. According to one embodiment, thecontrol scheme discussed in U.S. Pat. No. 7,318,347, titled“HEMISPHERICAL RESONATOR GYRO CONTROL”, filed on May 9, 2005, which isherein incorporated by reference in its entirety, is utilized tomaintain the total vibrational amplitude constant across the modes 400,420 while allowing the distribution of energy to transition freelybetween the modes 400, 420 subject to Coriolis forces.

The arrangement of the masses and flexures in the MEMS based gyroscopediscussed above result in a gyroscope that combines the best features ofa lumped element TF gyroscope and a rotationally symmetric gyroscope.The use of relatively large masses on relatively weak flexures enableslow damping, high momentum, and high sensitivity which may result in lowBrownian motion noise (the dominant resolution limit in MEMS basedsymmetric angular rate gyroscopes). The symmetrical eight massconfiguration enables the gyroscope to behave like a continuousrotationally symmetric vibratory gyroscope (e.g., such as a hemisphere,ring, or disc gyroscope). The mass-to-mass couplers cause the eightmasses to move in the n=2 vibratory mode, which is characterized by twoopposite masses 403 moving out (i.e., away from center), the twoopposite masses 405 (90° from the masses moving out) moving in (i.e., intowards the center), and the other four masses 407, 409 movingcircumferentially. This vibratory mode emulates the vibratory mode of arotationally symmetric gyroscope and is necessary so that the Coriolisforces, due to rotation about the Z axis, couple the two modes together,allowing the rate of rotation or the angle of rotation to be sensedbased on the vibrations of the masses.

The particular arrangement of the link between adjacent masses (i.e.,the mass-to-mass couplers 108 shown in FIG. 1) is important to ensuringthe correct modal structure of the gyroscope. For example, Applicant hasappreciated that in order to couple the two modes together, eachmass-to-mass coupler 108 must be stiff in the circumferential direction,yet compliant in the radial direction. For example, FIG. 5A is a diagramof one embodiment of a mass-to-mass coupler according to aspects of thepresent invention. The mass-to-mass coupler 108 includes a stiff “bar”111 that has a flexural hinge 109 on either side. The stiff “bar” 111operates such that the circumferential motion of a mass 102 to which itis coupled depends on the radial motion of the masses adjacent partner.Accordingly, as the masses 102 vibrate, the stiff “bar” 111 results inthe gyroscope 100 operating in the n=2 vibratory mode. In otherembodiments, any other type of mass-to-mass coupler can be used thatcouples masses together such that the radial and circumferential motionsof adjacent masses 102 act in such a way as to result in the n=2vibratory mode where two opposite masses 102 are moving radiallyoutward, two opposite masses 102 are moving radially inward, and themasses 102 located in between move circumferentially. For example,according to some embodiments, the structure of the mass-to-mass couplermay be configured differently (e.g., as discussed below with regard toFIG. 10), the gyroscope may include multiple mass-to-mass couplerscoupled between each adjacent mass (e.g., as discussed below with regardto FIG. 12), and in addition to being coupled between adjacent masses,the mass-to-mass coupler may also be coupled to a central anchor via aflexural hinge (e.g., as discussed below with regard to FIG. 16).According to some other embodiments, a mass-to-mass coupler includes aring (or rings) that are configured to couple all masses together (e.g.,as discussed below with regard to FIGS. 17-19).

According to at least one embodiment, the gyroscope 100 also includesangled electrodes 118 which enable the cross-spring term of the masses102 to be trimmed. The cross spring term in the gyroscopes 100 equationsof motion describes the mechanical coupling between modes 400, 420. Morespecifically, the cross spring term is a spring constant quantifying theamount of force applied in a direction that increases one modeproportionally in response to the motion of the other mode. It isadvantageous to reduce or eliminate this term as it is desirable to haveeach mode only be excited by rotation of the gyroscope 100. Typically,this coupling is intentionally minimized by the design of the suspension(i.e., the springs or flexures). However, fabrication imperfections maycause the cross spring term to be non-zero. In a rate mode of operation,this may result in a quadrature error when the demodulation phase isalso imperfect. As a result, standard TF gyroscopes typically tune outthe cross-spring term by compensating it with a variable bias applied tothe driver transducers (e.g., the drive combs).

In a whole-angle operating gyroscope, the cross-spring term may alsolead to errors. For example, the performance of a whole angle operatinggyroscope depends on the frequencies of two vibratory modes being equal.Reducing the frequency split between modes to zero is not possibleunless the cross spring term is also reduced to zero. Some existingwhole-angle-capable gyroscopes (e.g., such as a quad mass gyroscope)provide a capability of tuning only the on-axis spring term, and hencecannot achieve perfect mode matching. Such gyroscopes rely on themechanical cross-spring term being small by design. Other vibratory MEMSbased gyroscopes (e.g., such as ring gyroscopes) use electrostaticforcers located at specific locations to provide a tunable spring forcethat compensates for the mechanical cross spring term. None of the rateor whole angle based methods of compensating for the cross spring termare applicable to the gyroscope 100 discussed above. Accordingly, thegyroscope 100 includes the angled electrodes 118 which are configured totrim the cross-spring term of the masses 102.

Each angled electrode 118 is configured such that the electrodegenerates a radial force component in response to circumferential motionof a corresponding mass 102 and the electrode generates acircumferential force component in response to radial motion of thecorresponding mass 102. For example, as shown in FIG. 5A, in response tocircumferential motion 127 of a mass 102 (Mass 1), the electrode 118applies a radial force component 125 to the same mass 102 (Mass 1) andin response to radial motion 125 of the mass 102 (Mass 1), the electrode118 applies a circumferential force component 127 to the same mass 102(Mass 1). Similarly, in response to circumferential motion 123 of themass 102 (Mass 2), the electrode 118 applies a radial force component121 to the same mass 102 (Mass 2) and in response to radial motion 121of the mass 102 (Mass 2), the electrode 118 applies a circumferentialforce component 123 to the same mass 102 (Mass 2).

The magnitude of the circumferential and radial force components appliedby an electrode 118 depends on the voltage applied to the electrode 118.Each electrode 118 is angled such that circumferential or radial motionin one vibratory mode (e.g., vibratory mode 400 or 420) results in acorresponding circumferential or radial force in the other mode. Theresulting force, due to circumferential or radial motion, will eitherassist or oppose motion in the vibratory mode depending on whichelectrodes 118 are used and the voltages applied to them. Therefore, thecross spring term can be cancelled regardless of the polarity of thecross spring term.

According to one embodiment, the MEMS based gyroscope 100 is implementedon a substrate (e.g., substrate 430 shown in FIG. 4). In at least oneembodiment, the substrate 430 is a cubic crystal structure. Asillustrated in FIG. 5B, a cubic crystal structure (e.g., single crystalsilicon (Si)) exhibits anisotropic elastic properties such that flexuresoriented along the (100) direction plane behave differently fromflexures having the same geometry but oriented along the (110) directionplane (the (100) direction plane and the (110) direction plane being 45°apart). This causes errors in whole angle operation because the naturalfrequencies of the two vibratory modes will differ.

Historically the difference in moduli between the (100) direction andthe (110) direction has been compensated for by adjusting flexure width;however, in at least one embodiment, these modulus differences arecompensated for by rotating the entire device by 22.5° relative to the(100) direction plane. For example, as shown in FIG. 5C, whenconstructing the device, the geometry of the device is oriented relativeto the crystallographic orientation of silicon such that the (100) planefalls along direction 433 and the (110) plane falls along direction 435.This places the axis of the corresponding flexures (e.g., flexures A andB) along a line 502 that is halfway between the (100) direction plane433 and the (110) direction plane 435 (i.e., 22.5° between the (100) and(110) direction planes), rather than exactly on either the (100)direction plane 433 or the (110) direction plane 435. The result is thatall flexures having the same geometry have the same modulus, and willthus behave in the same way. This may save design time and also reduceerrors that arise from imperfect width-based compensation, which isoften attempted using simplified analytical models that imperfectlypredict the stiffness of complicated flexures. As discussed above, theMEMS based gyroscope 100 is implemented on a silicon based substrate;however, in other embodiments, the MEMS based gyroscope 100 can beimplemented on any type of cubic crystal structure.

In another embodiment, planar isoelasticity in a cubic crystal basedsubstrate (e.g., substrate 430) is achieved by utilizing a wafer with a(111) crystal orientation. For example, as shown in FIG. 5D, when thedevice is implemented on a cubic crystal based substrate 430 with a(111) crystal orientation, the in-plane directions are (110) and/or(112), all of which have the same modulus. The result is that allflexures having the same geometry will thus behave in the same waywithout requiring compensation (e.g., as described above with respect tothe (100) crystal orientation). FIG. 6A is a diagram illustratinganother embodiment of a MEMS based gyroscope 600 configured according toaspects of the present disclosure. The gyroscope 600 is the same asgyroscope 100 discussed above with regard to FIG. 1 except that thegyroscope 600 does not include outside anchors (e.g., such as outsideanchors 114 shown in FIG. 1) or outside shuttles (e.g., such as outsideshuttles 112 shown in FIG. 1). In addition, the internal shuttles 613are configured differently. A benefit of such a configuration is thatinternal stress (which may arise from such causes as thermal expansioncoefficient mismatches between the gyroscope material and the substratematerial connecting a central anchor 602 and any outside anchors) areavoided. Such thermal mismatches between materials connecting the twoanchors may result in the stretching of masses/flexures suspendedbetween the two anchors. By only including one central anchor 602 in thegyroscope 600, such stretching may be avoided. Additionally, the biasstability of the gyroscope 600 may be improved by reducing thetransmission of (unpredictable) external stresses on the gyroscope 600.However, by only including one central anchor 602, the force isolation(i.e., decoupling x- and y-motion as discussed above with regard to FIG.2) provided by the outer shuttles and anchors is eliminated.

FIG. 6B is a diagram illustrating another embodiment of a MEMS basedgyroscope 650 configured according to aspects of the present disclosure.The gyroscope 650 is similar to the gyroscope 600 discussed above withregard to FIG. 6A except that the gyroscope 650 does not include angledelectrodes (e.g., such as the angled electrodes 118 shown in FIG. 1),and the anchor 652, internal flexures 654, and internal shuttles 653 areconfigured differently. FIG. 6C is a diagram illustrating furtherdetails of the anchor 652, internal flexures 654, and internal shuttle653 of the gyroscope 650.

FIG. 6D is a diagram illustrating another embodiment of a MEMS basesgyroscope 660 configured according to aspects of the present disclosure.The gyroscope 660 is similar to the gyroscope 650 discussed above withregard to FIG. 6B except that the gyroscope 650 includes outer shuttles662, outer flexures 664, and outer anchors 666. FIG. 6E is a diagramillustrating further details of the outer shuttles 662, outer flexures664, and outer anchors 666. According to one embodiment, the internalshuttles 653 and outer shuttles 662 are identical. This may simplify thedesign process of the gyroscope 660 and also has the benefit of beingmore symmetric. The outer shuttles 662 and inner shuttles 653 are bothconfigured to move in a circumferential direction and not in a radialdirection (e.g., differently than discussed above with regard to FIG.1).

FIG. 6F is a diagram illustrating another embodiment of a MEMS basedgyroscope 680 configured according to aspects of the present disclosure.The gyroscope 680 is substantially the same as the gyroscope 660discussed above with regard to FIG. 6D except that the outer shuttles,outer flexures and outer anchors are configured differently. Forexample, as shown in FIG. 6F, the gyroscope 680 includes outer shuttles682, outer flexures 684, and outer anchors 686.

FIG. 7A is a diagram illustrating another embodiment of a MEMS basedgyroscope 700 configured according to aspects of the present disclosure.The gyroscope 700 is similar to the gyroscope 100 discussed above withregard to FIG. 1 except that the gyroscope 700 does not include outsideanchors or outside shuttles (e.g., as discussed above with regard toFIG. 6), does not include internal shuttles (e.g., such as internalshuttles 113 shown in FIG. 1) and the flexures 702 are configureddifferently in a serpentine configuration. FIG. 7B is a diagramillustrating the MEMS based gyroscope 700 and outer clapper electrodes704 adjacent each mass 701 of the gyroscope 700. The outer clapperelectrodes 704 are part of adjacent drive/sense transducers (e.g., thedrive/sense transducers 116 shown in FIG. 1) utilized to drive and sensemotion of the masses 701.

FIG. 8 is a diagram illustrating another embodiment of a MEMS basedgyroscope 800 configured according to aspects of the present disclosure.The gyroscope 800 is similar to the gyroscope 100 discussed above withregard to FIG. 1 except that the gyroscope 800 does not include outsideanchors or outside shuttles (e.g., as discussed above with regard toFIG. 6), does not include internal shuttles (e.g., such as internalshuttles 113 shown in FIG. 1) and the flexures 802 are configureddifferently in a stacked configuration. FIG. 9 is a diagram illustratingfurther details of the stacked configuration of flexures 802. Inaddition, unlike the mass-to-mass couplers 108 shown in FIG. 1, thegyroscope 800 utilizes different mass-to-mass couplers 804 to coupletogether adjacent masses. FIG. 10 is a diagram illustrating furtherdetails of a mass-to-mass coupler 804. The mass-to-mass coupler 804 ismore stiff in the radial direction and more soft in the circumferentialdirection.

FIG. 11 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1100 configured according to aspects of the presentdisclosure. The gyroscope 1100 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1100 does notinclude outside anchors or outside shuttles (e.g., as discussed abovewith regard to FIG. 6), does not include internal shuttles (e.g., suchas internal shuttles 113 shown in FIG. 1) and the flexures 1102 areconfigured differently in a serpentine configuration. In addition,unlike the mass-to-mass couplers 108 shown in FIG. 1, the gyroscope 1100utilizes mass-to-mass flexures 1104 (e.g., as shown in FIG. 10) tocouple together adjacent masses.

FIG. 12 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1200 configured according to aspects of the presentdisclosure. The gyroscope 1200 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1200 includes twomass-to-mass couplers 1208 coupled between each adjacent mass 1202, andthe flexural hinges on the couplers are straight instead of folded.

FIG. 13 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1300 configured according to aspects of the presentdisclosure. The gyroscope 1300 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1300 does notinclude outside anchors (e.g., such as outside anchors 114 shown inFIG. 1) or outside shuttles (e.g., such as outside shuttles 112 shown inFIG. 1), and the internal flexures 1314, internal shuttles 1313, andanchor 1312 are configured differently. For example, as shown in FIG.13, the internal shuttles 1313 are extended length shuttles.

FIG. 14 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1400 configured according to aspects of the presentdisclosure. The gyroscope 1400 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1400 does notinclude outside anchors (e.g., such as outside anchors 114 shown inFIG. 1) or outside shuttles (e.g., such as outside shuttles 112 shown inFIG. 1), and the internal flexures 1414, internal shuttles 1413, andanchor 1412 are configured differently. For example, as shown in FIG.14, each mass 1402 includes two extended length internal shuttles 1413and the anchor 1412 extends into each mass 1402.

FIG. 15 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1500 configured according to aspects of the presentdisclosure. The gyroscope 1500 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1500 does notinclude outside anchors (e.g., such as outside anchors 114 shown inFIG. 1) or outside shuttles (e.g., such as outside shuttles 112 shown inFIG. 1), and the internal flexures 1514, internal shuttles 1513, anchor1512, and mass-to-mass couplers 1508 are configured differently. FIG. 16is a diagram illustrating further detail regarding the internal flexures1514, internal shuttles 1513, anchor 1512, and mass-to-mass coupler1508. The anchor 1512 extends between each mass 1502. The mass-to-masscoupler 1508 includes a “stiff” bar 1510 that is coupled betweenadjacent masses 1502 via flexural hinges 1509. The bar 1510 is alsocoupled to the anchor 1512 via a flexural hinge 1511.

FIG. 17A is a diagram illustrating another embodiment of a MEMS basedgyroscope 1700 configured according to aspects of the presentdisclosure. The gyroscope 1700 is similar to the gyroscope 100 discussedabove with regard to FIG. 1 except that the gyroscope 1700 does notinclude outside anchors (e.g., such as outside anchors 114 shown inFIG. 1) or outside shuttles (e.g., such as outside shuttles 112 shown inFIG. 1), and the internal flexures 1714, anchor 1712, and mass-to-masscouplers are configured differently. As shown in the gyroscope 1700 ofFIG. 17, the mass-to-mass coupler includes an internal ring 1708 and anexternal ring 1710 which are configured to couple together adjacentmasses 1702. For example, FIGS. 17B and 17C are diagrams illustratingfurther detail of the internal ring 1708 and the external ring 1710.According to one embodiment, the internal ring 1708 and external ring1710 are single continuous rings. In another embodiment, the internalring 1708 may include multiple independent portions, each portionconfigured to couple together two adjacent masses 1702. Similarly, theexternal ring 1710 may include multiple independent portions, eachportion configured to couple together two adjacent masses 1702.

FIG. 18 is a diagram illustrating another embodiment of a MEMS basedgyroscope 1800 configured according to aspects of the presentdisclosure. The gyroscope 1800 includes a plurality of masses 1802. Eachmass 1802 is suspended between two shuttles 1804 via flexures 1806. Eachmass is also coupled to a ring 1808. The gyroscope 1800 operates insubstantially the same way as the gyroscope 100 discussed above withregard to FIG. 1 except that with the gyroscope 1800, the ring 1808 actsas the mass-to-mass coupler. FIG. 19 is a diagram illustrating furtherdetails of the mass 1802, shuttles 1804, and flexures 1806.

As discussed above, in certain embodiments, the MEMS based gyroscopeincludes eight masses; however, in other embodiments, the MEMS basedgyroscope may include any number of masses. For example, in oneembodiment, the MEMS based gyroscope includes any number of masses thatis greater than eight and a multiple of four. As also discussed above,the MEMS based gyroscope includes wedge-shaped masses; however, in otherembodiments, the masses may be configured in any appropriate shapecapable of operating in the n=2 vibratory mode.

As discussed above, the MEMS based gyroscope is operated in an n=2vibratory mode; however, in other embodiments, the MEMS based gyroscopemay be operated in some other vibratory mode. For example, in at leastone embodiment, the MEMS based gyroscope includes 12 masses and isconfigured to operate in the n=3 vibratory mode. In other embodiments,the MEMS based gyroscope may be configured to operate in any othervibratory mode (e.g., n=3 vibratory mode, n=4 vibratory mode, n=5vibratory mode, etc.) and may include an appropriate number of masses.

A new MEMS based gyroscope design is provided that combines the bestfeatures of a lumped element TF gyroscope and a rotationally symmetricgyroscope. The new design efficiently uses relatively large masses(e.g., like a TF gyroscope) on relatively weak flexures to provide highsensitivity while maintaining an eight-fold symmetry conducive to then=2 vibratory mode used in most whole angle based gyroscopes to providehigh dynamic range. The new design is capable of operating in both rateand whole angle mode, is low cost, and is easily fabricated.

According to one embodiment, the MEMS based gyroscope design discussedabove may be utilized as a whole angle gyroscope in a miniature system.In another embodiment, the MEMS based gyroscope may be utilized as awhole angle gyroscope in a platform having a high rotation rate thatrequires a high dynamic range instrument. The MEMS based gyroscope maybe utilized in any other whole angle application.

The MEMS based gyroscope design could also be used in any applicationwhere traditional MEMS gyroscopes are currently used. The combination oflarge masses on weak springs (providing high momentum and low damping)and matched modes (providing high gain) yields a low Angle Random Walk(ARW), one of the primary performance parameters for gyroscopes.Applicant has appreciated that an ARW on the order of 0.01 deg/rt-hrwill be obtained with this gyroscope design and improvement of 10× (ormore) could be possible by increasing the size of the gyroscope.

Various embodiments of systems and methods disclosed herein may haveapplications in various fields. Applications may encompass the field ofprecision inertial guidance and navigation, particularly in GPS deniedenvironments. For example, embodiments may be used to guide platformssuch as strategic missiles, submarines, Unmanned Underwater Vehicles(UUV), Unmanned Aerial Vehicles (UAV), cruise missiles, aircraft, andtactical munitions. Other examples of applications may includecommercial aviation, self-driving vehicles, robotic machinery, personalnavigation and consumer electronics such as various computing devicesand mobile communication devices.

Having described above several aspects of at least one embodiment, it isto be appreciated various alterations, modifications, and improvementswill readily occur to those skilled in the art. Such alterations,modifications, and improvements are intended to be part of thisdisclosure and are intended to be within the scope of the disclosure.Accordingly, the foregoing description and drawings are by way ofexample only, and the scope of the disclosure should be determined fromproper construction of the appended claims, and their equivalents.

What is claimed is:
 1. A gyroscope comprising: a central anchor; aplurality of internal flexures; a plurality of masses configured tovibrate in a first vibratory mode and a second vibratory mode, each masscoupled to the central anchor via at least one of the plurality ofinternal flexures and configured to translate in a plane of thegyroscope; a plurality of mass-to-mass couplers, each mass-to-masscoupler coupled between two adjacent masses of the plurality of masses;and a plurality of transducers configured to drive the plurality ofmasses and sense motion of the plurality of masses; wherein theplurality of transducers is configured to drive the plurality of massesin at least the first vibratory mode and the second vibratory mode. 2.The gyroscope of claim 1, wherein each transducer is located at aperiphery of a corresponding one of the plurality of masses.
 3. Thegyroscope of claim 2, wherein at least one transducer is configured toelectrostatically drive motion of its corresponding one of the pluralityof masses.
 4. The gyroscope of claim 2, wherein at least one transduceris configured to magnetically drive motion of its corresponding one ofthe plurality of masses.
 5. The gyroscope of claim 2, wherein at leastone transducer is configured to optically drive motion of itscorresponding one of the plurality of masses.
 6. The gyroscope of claim2, wherein at least one transducer is configured to piezoelectricallydrive motion of its corresponding one of the plurality of masses.
 7. Thegyroscope of claim 2, wherein at least one transducer is configured tothermally drive motion of its corresponding one of the plurality ofmasses.
 8. The gyroscope of claim 1, wherein the plurality oftransducers is further configured to drive the plurality of masses in ann=2 vibratory mode.
 9. The gyroscope of claim 8, wherein the firstvibratory mode and the second vibratory mode are 45° apart.
 10. Thegyroscope of claim 8, wherein the plurality of transducers is furtherconfigured to drive motion of the plurality of masses at a fixedamplitude in the first vibratory mode and to sense motion of theplurality of masses in the second vibratory mode.
 11. The gyroscope ofclaim 10, further comprising a controller coupled to the plurality oftransducers, wherein the plurality of transducers is further configuredto provide signals to the controller based on the sensed motion of theplurality of masses in the second vibratory mode, and wherein thecontroller is configured to calculate a rate of rotation of thegyroscope based on the signals.
 12. The gyroscope of claim 8, whereinthe plurality of transducers is further configured to drive motion ofthe plurality of masses such that a total vibrational energy ismaintained across the first vibratory mode and the second vibratory modeand to sense a distribution of energy between the first vibratory modeand the second vibratory mode.
 13. The gyroscope of claim 12, furthercomprising a controller coupled to the plurality of transducers, whereinthe plurality of transducers is further configured to provide signals tothe controller based on the sensed distribution of motion between thefirst vibratory mode and the second vibratory mode, and wherein thecontroller is configured to calculate an angle of rotation of thegyroscope based on the signals.
 14. The gyroscope of claim 1, whereineach mass-to-mass coupler includes a bar coupled to each adjacent massvia a flexural hinge, wherein the bar is configured to operate such thatcircumferential motion of one of the two adjacent masses of theplurality of masses to which it is coupled depends on radial motion ofthe other one of the two adjacent masses.
 15. The gyroscope of claim 1,further comprising: a plurality of outside anchors; a plurality ofoutside shuttles, each located at a periphery of a corresponding one ofthe plurality of masses; and a plurality of outside flexures; whereineach mass of the plurality of masses is suspended between the centralanchor and the plurality of outside anchors via the plurality ofinternal flexures and the plurality of outside flexures; and whereineach one of the plurality of outside shuttles is configured to restrictrotation of its corresponding one of the plurality of masses.
 16. Thegyroscope of claim 15, wherein each one of the plurality of outsideshuttles is further configured to decouple x- and y-motion of itscorresponding one of the plurality of masses.
 17. The gyroscope of claim15, wherein each one of the plurality of outside shuttles is furtherconfigured to prevent force from being applied circumferentially to itscorresponding one of the plurality of masses.
 18. The gyroscope of claim1, further comprising a plurality of internal shuttles, each one of theplurality of internal shuttles coupled between the central anchor and acorresponding one of the plurality of masses and configured to restrictrotation of its corresponding one of the plurality of masses.
 19. Thegyroscope of claim 18, wherein each one of the plurality of internalshuttles is further configured to decouple x- and y-motion of itscorresponding one of the plurality of masses.
 20. The gyroscope of claim1, further comprising a plurality of angled electrodes, each angledelectrode coupled to a corresponding one of the plurality of masses andconfigured to trim the cross spring term of the corresponding one of theplurality of masses.
 21. The gyroscope of claim 20, wherein in trimmingthe cross spring term of its corresponding one of the plurality ofmasses, each angled electrode is configured to: generate a radial forcecomponent in the second vibratory mode in response to a circumferentialmotion of its corresponding one of the plurality of masses in the firstvibratory mode; and generate a circumferential force component in thesecond vibratory mode in response to a radial motion of itscorresponding one of the plurality of masses in the first vibratorymode; wherein the radial force component and the circumferential forcecomponent are configured to either assist or oppose the vibration of theplurality of masses in the second vibratory mode to trim the crossspring term.
 22. The gyroscope of claim 1, wherein the gyroscope isimplemented on a cubic crystal based substrate having a (100) directionplane and a (110) direction plane; and wherein at least one of theplurality of internal flexures is oriented equidistant from the (100)direction plane and the (110) direction plane.
 23. The gyroscope ofclaim 22, wherein the at least one of the plurality of internal flexuresis oriented 22.5° from the (100) direction plane and the (110) directionplane of the cubic crystal-based substrate.
 24. The gyroscope of claim22, wherein the cubic crystal-based substrate is a Silicon (Si) basedsubstrate.
 25. The gyroscope of claim 1, wherein the plurality of massesincludes a plurality of wedge-shaped masses.
 26. The gyroscope of claim1, wherein the plurality of masses is arranged symmetrically about thecentral anchor.
 27. The gyroscope of claim 1, wherein the gyroscope hasa thickness, and wherein the plurality of internal flexures includesflexures having a width that is at least five times narrower than thethickness of the gyroscope.
 28. The gyroscope of claim 1, wherein thegyroscope is a Microelectromechanical System (MEMS) based gyroscope. 29.A gyroscope comprising: a central anchor; a plurality of internalflexures; a plurality of masses configured to vibrate in a vibratorymode emulating the n=2 vibratory mode of a rotationally symmetricgyroscope, each mass coupled to the central anchor via one of theplurality of internal flexures and configured to translate in a plane ofthe gyroscope; means for driving the plurality of masses in thevibratory mode emulating the n=2 vibratory mode of a rotationallysymmetric gyroscope; and means for operating the gyroscope in one of arate mode of operation or a whole angle mode of operation.
 30. Thegyroscope of claim 29, further comprising means for decoupling radialand circumferential motion of each one of the plurality of masses. 31.The gyroscope of claim 29, further comprising means for trimming a crossspring term of the gyroscope.